LETTER TO THE GOVERNMENTS OF THE EU MEMBER STATES In the last few years there has been an intense discussion on the voting procedure in the Council of Ministers of the European Union. With 25 member states (and two more in the near future) it is not a simple task to make reliable judgements on the implications of the various voting systems that have been suggested. We the undersigned wish to draw the attention of EU Governments to the fact that scientific methods can be used and need to be used to analyse, understand and design complex voting systems. In particular: 1) From a scientific point of view there are obvious drawbacks to the systems of voting in the European Council discussed so far. The experts on voting theory agree that the Treaty of Nice gives too much power to a number of countries while others obtain less power than appropriate. On the other hand, the draft European Constitution assigns too much power to the biggest and the smallest states in a systematic way, while the middle size countries do not get their due share of influence (see the tables attached). Moreover, the Nice system will be extremely ineffective due to its high quotas. 2) The ‘compromises’ proposed recently to change the quota in the draft Constitution either to 65% of the population and 55% of the states or to 55% of the population and 55% of the states make the situation for several countries even worse than in the draft Constitution. As can be shown by mathematical analysis, it is not the quotas that are mainly at fault, but rather the system of proposed weights. 3) The basic democratic principle that the vote of any citizen of a Member State ought to be worth as much as for any other Member State is strongly violated both in the voting system of the Treaty of Nice and in the rules given in the draft Constitution. It can be proved rigorously that this principle is fulfilled if the influence of each country in the Council is proportional to the square root of its population. This is known as ‘Penrose’s Square Root Law’. Such a system may be complemented by a simple majority of states. 4) A voting system that obeys the Square Root Law, i.e., which gives equal power to all citizens, is easily implemented. It is representative, objective, transparent, and effective. Such a system was proposed by Swedish diplomats already in 2000, and recently endorsed in a number of scientific articles. We urge our politicians to take into consideration the contribution of the scientific community to this issue. We are highly concerned that any system implemented without due regard to the scientific analysis of voting power may become a major drawback to a democratic development in the European Union. 1 TABLES 2,0% i 1,5% 1,0% 0,5% 0,0% -0,5% -1,0% Differences in the Banzhaf -1,5% Germany France U.K. Italy Spain Poland Netherlands Greece Portugal Belgium Czech Republic Hungary Sweden Austria Denmark Slovakia Finland Irleland Lithuania Latvia Slovenia Estonia Cyprus Luxembourg Malta Diagram 1. Differences in voting power in the EU Council between the square root law and the procedure of the Treaty of Nice 1,5% 1,0% 0,5% 0,0% -0,5% -1,0% -1,5% -2,0% -2,5% Differences in the Banzhaf -3,0% -3,5% Germany France U.K. Italy Spain Poland Netherlands Greece Portugal Belgium Czech Republic Hungary Sweden Austria Denmark Slovakia Finland Irleland Lithuania Latvia Slovenia Estonia Cyprus Luxembourg Malta Diagram 2. Differences in voting power in the EU Council between the square root law and the proposal of the Draft Constitution 2 Signed by Scientists for a democratic Europe Prof. Dr. Jesús Mario Bilbao University of Seville, Spain. [email protected] Dr. Frédéric Bobay, Economist and civil servant, Paris, France. [email protected] Dr. Stefan Böcker, WestLB AG, Düsseldorf, Germany. [email protected] Prof. Dr. Anne Boutet de Monvel, Université de Paris 7, France. [email protected] Prof. Dr. David A. Brannan, The Open University, United Kingdom. [email protected] Dr. Francesc Carreras, Polytechnic University of Catalonia, Barcelona, Spain. [email protected] Prof. Dr. Jean Michel Combes, Université du Sud Toulon-Var, France. [email protected] Prof. Dr. Harrie C. M. de Swart, Tilburg University, Netherlands. [email protected] Prof. Dr. Peter Eichelsbacher, Ruhr-University of Bochum, Germany. [email protected] Dr. rer. nat. Martin Fehndrich, Wahlrecht.de, Duisburg, Germany. [email protected] Dr. Josep Freixas, Polytechnic University of Catalonia, Barcelona, Spain. [email protected] Dr. Uwe Grimm, The Open University, United Kingdom. [email protected] Prof. Dr. Fritz Haake, University of Duisburg-Essen, Germany. [email protected] Prof. Dr. Madeleine O. Hosli, Leiden University, Netherlands. [email protected] Prof. Dr. Alan Huckleberry, Ruhr-University of Bochum, Germany. [email protected] Prof. Dr. Thomas Jahnke, University of Potsdam, Germany. [email protected] Prof. Dr. Ladislav Kabat, Comenius University, Bratislava, Slovakia. [email protected] Prof. Dr. Werner Kirsch Ruhr-University of Bochum, Germany. [email protected] Prof. Frédéric Klopp Université Paris-Nord, France. [email protected] Priv.-Doz Dr. Vadim Kostrykin Fraunhofer Institute for Laser Technology, Aachen, Germany. [email protected] Prof. Dr. Dominique Lepelley, Université de Caen Basse-Normandie, France. [email protected] Prof. Dr. Moshé Machover, London School of Economics, United Kingdom. [email protected] Dr. Antoni Magaña, Polytechnic University of Catalonia, Barcelona, Spain. [email protected] 3 Dipl.-Math. Stefan Maus, University of Maastricht, Netherlands. [email protected] Dipl.-Wi.-Ing. Oliver Mayer, University of Karlsruhe, Germany. [email protected] Prof. Iain McLean, Oxford University, United Kingdom. [email protected] Priv.-Doz. Dr. Peter Müller, Göttingen University, Germany. [email protected] Dr. Stefan Napel, University of Hamburg, Germany. [email protected] Priv.-Doz. Dr. Norbert Peyerimhoff, Ruhr-University Bochum, Germany. [email protected] Dr. Bela Plechanovová, Charles University, Prague, Czech Republic. [email protected] Prof. Dr. Friedrich Pukelsheim, University of Augsburg, Germany. [email protected] Prof. Victoriano Ramírez Gonzáles, Granada University, Spain. [email protected] Prof. Dr. Rudolf A. Roemer, University of Warwick, United Kingdom. [email protected] Dr. Agnieszka Rusinowska, Warsaw School of Economics, Poland. [email protected] Prof. Dr. Pieter H.M. Ruys, Tilburg University, Netherlands. [email protected] Prof. Maurice Salles, Université de Caen Basse-Normandie, France [email protected] Prof. M. Remzi, Sanver Bilgi University, Istanbul, Turkey. [email protected] Dr. Bernd Sing, University of Bielefeld, Germany. [email protected] Dr. Wojciech Słomczyński, Jagiellonian University, Poland. [email protected] Dr. Tadeusz Sozański, Jagiellonian University, Poland. [email protected] Prof. Dr. Bernard Steunenberg, Leiden University, Netherlands. [email protected] Prof. Dr. Peter Stollmann, Technical University Chemnitz, Germany. [email protected] Prof. Dr. José Ignacio Torreblanca, Universidad Nacional de Educación a Distancia, Spain. [email protected] Dr. Ivan Veselic, California Institute of Technology, USA. [email protected] Dr. Simone Warzel Princeton University, USA. [email protected] Prof. Tomasz Zastawniak University of Hull, United Kingdom. [email protected] Dr. hab. Karol Życzkowski Jagiellonian University, Poland. [email protected] 4 .